Grade 6 math

Units

1. 1

   Ratios and rates

   5 lessons

   1. Ratio language and notationWrite ratios in the named order and distinguish a part-to-part ratio from a fraction of the whole.
   2. Equivalent ratios with tables, double number lines and graphsFind and check equivalent ratios using tables, aligned number lines and graphs.
   3. Unit rates, unit pricing and constant speedFind unit rates to compare prices and calculate distance at constant speed.
   4. Percent as a rate per 100Use a percent bar to find a part or a whole.
   5. Converting measurement units with ratiosConvert measurements and rates using equal-unit ratios, then check whether each count should grow or shrink.
2. 2

   Dividing fractions

   2 lessons

   1. What it means to divide by a fractionUse tapes to count fractional-size groups, find a whole from a known part, and name a partial group.
   2. Dividing fractions: the reciprocal method and why it worksDivide fractions and explain why multiplying by the divisor’s reciprocal gives the number of equal groups.
3. 3

   Multi-digit numbers and decimals

   3 lessons

   1. Dividing multi-digit numbers with the standard algorithmDivide multi-digit whole numbers by place value and check the result.
   2. Adding, subtracting, multiplying and dividing decimalsCalculate with decimals using place value and check whether answers are reasonable.
   3. Factors, multiples, GCF, LCM and the distributive propertyMatch pack totals, make the greatest number of identical bags, and rewrite a sum using its GCF.
4. 4

   Negative numbers and the coordinate plane

   3 lessons

   1. Positive and negative numbers, opposites and zeroPlace positive and negative numbers on a number line and find their opposites.
   2. Ordering rational numbers and absolute valueOrder signed rational numbers and explain how absolute value differs from signed value.
   3. The coordinate plane in four quadrantsPlot points, reflect them across an axis, and measure horizontal or vertical distances.
5. 5

   Expressions

   4 lessons

   1. Whole-number exponentsExpand and evaluate whole-number powers, including powers in longer calculations.
   2. Writing and reading expressions with variablesWrite expressions from words and name variables, terms, factors, coefficients, and constants.
   3. Evaluating expressions and formulasSubstitute given values into expressions and formulas, then calculate in the correct order.
   4. Equivalent expressions: properties, distributing and combining like termsRewrite expressions by combining like terms, distributing, or factoring, and explain why the value stays the same.
6. 6

   Equations and inequalities

   3 lessons

   1. Solutions as values that make a statement trueTest whether a value makes an equation or inequality true by substituting and comparing both sides.
   2. Writing and solving one-step equationsDraw a tape, write a one-step equation, solve it, and check the answer.
   3. Inequalities x > c and x < c on the number lineWrite inequalities for limits and graph their solutions, including whether the limit itself counts.
7. 7

   Two quantities that change together

   1 lesson

   1. Independent and dependent variables with tables, graphs and equationsIdentify the chosen and resulting quantities, then make a table, equation, and graph that agree.
8. 8

   Area, surface area and volume

   4 lessons

   1. Area of triangles, parallelograms, trapezoids and other polygonsFind polygon areas using perpendicular heights and by rearranging, adding, or subtracting simpler shapes.
   2. Volume of right rectangular prisms with fractional edgesFind a box’s volume from fractional edge lengths and explain it using cubes or base-area layers.
   3. Polygons in the coordinate planePlot a polygon, measure horizontal and vertical sides, and find area by splitting it into familiar shapes.
   4. Nets and surface areaDraw a solid’s net and add every face area to find its surface area.
9. 9

   Statistics

   4 lessons

   1. Statistical questions and distributionsIdentify statistical questions and describe a distribution’s center, spread, and shape.
   2. Measures of center: mean and medianCalculate mean and median, then choose which better describes a typical value when one value is far from the rest.
   3. Dot plots, histograms and box plotsMake and interpret three displays of reaction times, reporting the number of students and the units.
   4. Measures of variability: range, IQR and mean absolute deviationCalculate three measures of spread and use a matching center–spread pair to compare scores.